$\displaystyle \int sec^45x dx$

$\displaystyle =\int (sec^25x)(sec^25x) dx$

$\displaystyle =\int (1+tan^25x)sec^25x dx$

$\displaystyle =\int (sec^25x + tan^25xsec^25x)dx$

$\displaystyle =\int sec^25x dx + \int tan^25xsec^25x dx$

$\displaystyle =\frac{1}{5}tan5x + ??????$

I don't know what to do with the second integral, or if I am even starting this problem the right way. I have the solution, but it is missing all of the steps past the trig identity. TIA.